Rf resonance electron excitation

ABSTRACT

Apparatus and method for providing a resonant excitation of electrons to a predetermined narrow energy band using a magnetic and a DC electric field to form a confining region for electrons and an RF electrical signal for excitation of the electrons in the resonance mode. The DC and RF parameters and electrode configuration are predetermined so that the RF signal is in resonance with the natural frequency of electrons in the confining region when they are in a given energy range so as to produce a desired narrow electron energy distribution.

United States Patent [1 1 Karras RFRESONANCE ELECTRON EXCITATION [75] Inventor: Thomas W. Karras, Berwyn, Pa.

[73] Assignee: General Electric Company, New

York, NY.

[22] Filed: Jan. 16, 1973 [2]] Appl. No.: 324,154

Related US. Application Data [63] Continuation of Ser. No. 146,442, May 24 I97], abandoned, which is a continuation-in-part of Ser.

No. 800,799, Jan. 23, 1969, abandoned.

52 us. (:1. 331/94.5 PE, 331/945 0 51 Int. 01 H0lr 3/00 58 Field of Search..... 331/945 c, 94.5 D, 94.5 0,

[56] References Cited OTHER PUBLICATIONS Karras: Radio Frequency Breakdown in Penning Ge- Mar. 26, 1974 ometries with Nonbinear Fields, Journ. of Applied Physics, vol. 37, pp. 2782-2786, June, 1966.

Primary ExaminerEdward S. Bauer Attorney, Agent, or Firm-Henry W. Kaufmann; Allen F. Amgott; Raymond H. Quist 57 ABSTRACT Apparatus and method for providing a resonant excitation of electrons to a predetermined narrow energy band using a magnetic and a DC electric field to form a confining region for electrons and an RF electrical signal for excitation of the electrons in the resonance mode. The DC and RF parameters and electrode configurationare predetermined so that the RF signal is in resonance with the natural frequency of electrons in the confining region when they are in a given energy range so as to produce a desired narrow electron energy distribution.

2 Claims, 6 Drawing Figures PAIENTEHI-ARZSIBH I 3.800.244

' sum 2 or 3 INVENTOR. THo/v/As W. KARRAs,

BY 20% 4M AGENT THOMAS W. KARRAs,

BY MMA M AGENT RF RESONANCE ELECTRON EXCITATION CROSS-REFERENCE TO RELATED APPLICATION This application is a continuation of my copending application Ser. No. 146,442 filed May 24, I97], and now abandoned; which was a continuation-in-part of and copending with my earlier application Ser. No. 800,799, filed Jan. 23, 1969 and now abandoned, both of said applications having been entitled RF Resonance Electron Excitation.

BACKGROUND OF THE INVENTION The subject invention relates to the field of electron excitation, and particularly to excitation of electrons to a narrow energy band.

In the past, pumping of gas lasers to achieve laser action has been'primarily done by standard electrical discharge including RF discharge. Other techniques, such as high intensity light flashes, flame or electron beam pumping have been tried, but have not been used to any great extent. Also, these prior art pumping schemes are only useful in a relatively limited pressure range of operation and have not been successful at low gas pressures. The energy efficiencies for gas lasers have been extremely low, generally a small fraction of a percent and extending only in a few cases to an efficiency over percent. These low efficiencies have been primarily due to energy losses associated with the loss of energizing electrons to the walls and unnecessary excitation of energy levels besides those of the lasing system.

It is known that electron excitation can be caused by RF resonance, but controlled utilization of such an excitation technique prior to the subject invention had not been accomplished.

SUMMARY'OF THE INVENTION to provide method and apparatus for exciting electrons to a narrow energy range.

A further object of the subject invention is to provide a gas laser having greatly improved efficiency.

Another object of the subject invention is to provide a gas laser capable of operation at a low gas pressure.

Still another object of the subject invention is to provide a gas laser pumping apparatus and method which is capable of selectively exciting a specific energy level of the background gas.

Yet another object is to provide a method and apparatus for controlling energization of electrons by resonant excitation.

In order to fulfill the above-mentioned objects the subject invention provides a method and apparatus for providing controlled energization of electrons for use in a variety of devices such as a gas laser, infrared or ultraviolet lamp, including means for providing both and electric and magnetic field within the device to confine the electrons to a given region. A source of electrons such as an easily ionized impurity or a hot filament is preferably located within the device. The pertinent parameters of the apparatus are selected so that electrons within the confined region are energized in the resonance mode by a DC-biased RF discharge.

Due to the electromagnetic fields the electrons are sions with the background gas and is thus very small. Excitation in the resonance mode, which results from a resonance between the applied oscillator frequency and natural electron frequency causes the electrons to be energized very rapidly without need of collisions and the electron energy can be limited to some maximum value and held there for a large fraction of the electron transit time. This allows excitation of higher atomic and molecular energy states without affecting those below these states. I

This subject matter which is regarded as the subject invention is particularly pointed out and distinctly claimed in the concluding portion of this specification.

BRIEF DESCRIPTION OF THE DRAWINGS The subject invention, however, together with further objects and advantages thereof, may best be understood by reference to the following description taken in connection with the accompanying drawings in which:

FIG. 1 is a side sectional view of one embodiment of gas laser utilizing the subject invention;

FIG. 2 is a Mathieu stability chart;

FIG. 3 is a side sectional view of a second embodiment of gas laser utilizing the subject invention;

FIG. 4 is a perspective view of the preferred embodiment of a gas laser utilizing the subject invention;

FIG. 5 is a perspective view of a portion of the embodiment shown in FIG. 4; and

FIG. 6 is a cross-sectional view of the apparatus shown in FIG. 4 taken along the line denoted VI--VI.

DESCRIPTION OF THE PREFERRED EMBODIMENTS A simplified view of a gas laser in accordance with the subject invention is shown in FIG. 1. The gas laser 10 includes aglass-wall airtight enclosure 12 formed of two coaxial substantially cylindrical shaped members 12a, 12b and two reflectors (mirrors) l4, 16 closing the ends of the glass enclosure member 12 and sealed thereto to prevent leakage of air into the area within the enclosure 12, i.e., the laser interior. Adjacent the side of each of the reflectors I4, 16 opposite the interior, laser cathodes 18, 20 are respectively located. Reflector 16 is of substantially 100 percent reflectivity, and reflector I4 is of a reflectivity somewhat less than 100 percent. Cathode 18 adjacent reflector 14 has at least one aperture 22 therein with a high transparency screen 24 located across it. Electromagnetic radiation from the laser interior is allowed to exit from the laser 10 through the screen 24.

Cathodes 18, 20 are electrically connected to an output terminal of DC biased oscillator 26 which produces an RF electric signal superimposed on a DC electric field. Cathodes 18, 20 act as electrodes for the RF sigkept within the confined region, so that the loss rate of the electrons is determined almost exclusively by collinal as well as cathode electrodes for the DC field. Electrical connection is made from the remaining terminal of the oscillator to an anode 28 which in this embodiment is of a circular disc shape with an aperture 30 in the center thereof. Anode 28 acts as the anode-for the DC field and as an electrode for the RF signal. Anode 28 is substantially parallel to and midway between reflectors 14, 16 and joined between the two adjacent ends of enclosure members 12a, b with a portion of anode 28 extending within the interior of the laser.

Also, suitable means for providing a magnetic field within the interior of the laser is provided. In the embodiment shown in FIG. 1 this means is in the form of a solenoid 32 having coils thereof located substantially parallel to and outside laser enclosure 12. Located in enclosure wall 12 is an inlet 34 to which is connected a gas control system 36 which evacuates and fills the interior of the laser with the desired gas or gases.

For operation of laser 10 any suitable lasing gas such as argon, mercury, helium, etc. may be used preferably along with a small percentage of an easily ionized impurity, such as cesium vapor, is added to the laser gas, for example, argon, in very small quantity to provide electrons for the excitation process. Alternatively, a hot filament could be used to produce the necessary electrons. The interior of the laser is first evacuated by means of gas control system 36 and is filled with argon gas to a pressure in the range of l l mm Hg and cesium to a partial pressure in the range of about l0 l0 mm Hg. Solenoid 32 is connected to a suitable electrical power source to provide a substantially uniform magnetic field within the interior of laser 10 and centered within aperture 30 in the anode. A DC voltage source, not shown, of a predetermined amplitude is impressed across anode 28 and cathodes 18, to create an electric field whose configuration is determined by the electrode structure. Together, the magnetic and electric fields form an electron confining region. An RF voltage generated by oscillator 26 is superimposed on the DC voltage and forms a continuously varying field within laser 10 across the electron confining region. Stray electrons located within the electron confining region are resonantly excited by the RF field causing ionization of the cesium vapor and excitation and population inversion of the argon vapor. This in turn causes lasing action to take place. As a result of the lasing ac tion, a beam of energy exits from the laser through the transparent screen 24. This resonant excitation is explained in greater detail below.

Excitation is basically effected by the periodic variation of the depth of the electrostatic potential well formed by the electric and magnetic fields causing the electrons confined therein to gain energy. This periodic variation is caused by the RF energy input across elec-' trodes l6, 18, 28. Two modes of energy gain can result from the aforementioned type of excitation. One, called the collisional mode, requires collisions for electron energy gain to occur. The rate of energy growth is proportional to the collision frequency. The second, called the resonance mode, operates without collisions and results from a resonance between the applied oscillator frequency and the natural electron frequency in the electrostatic well. The resonance mode causes a growth rate proportional to the applied frequency and so can thereby energize electrons much more rapidly than the collisional mode. Also, because the collisional mode, of necessity, involves collisions, it cannot be used for excitation of anything but the lowest atomic or molecular energy states. The resonance mode, however, can be used for excitation of the higher atomic or molecular states without affecting lower states if collisions are prevented until after the proper energy has been reached. The use of a high applied RF frequency will minimize the time electrons remain at these lower energies, due to the rapid energy growth rate and so minimize the number of interfering collisions. Once the electrons have gained energy to the desired energy level, the energy growth process is arrested, as explained below. These electrons will then excite selectively atoms and molecules in the background gas to a quantum state corresponding to the electron energy level. A population inversion is thus efficiently produced due to optimum energy utilization by preventing energy loss due to excitation of lower and higher energy states.

The means of limiting electron energy gain can best be explained by reference to a Mathieu stability chart as shown in FIG. 2. Determination of the mode of energy growth for a given set of parameters can be obtained from this chart by noting that for coordinates in unstable regions, only the resonance mode of excitation can occur, while in stable regions, only the collisional mode of excitation can occur. This analysis is described in an article by the inventor of the subject invention entitled Radio Frequency Breakdown in Penning Geometries with Nonlinear Fields," in Journal of Applied Physics, Vol. 37, No. 7, 2782-2786, June 1966.

On the chart the abscissa is specified by the parameter a which is a function of V (the applied DC voltage) and the ordinate by the parameter q which is a function of V (the applied RF voltage amplitude). Parameters a and q are fixed by the values of the constants in the equations of motion for the electron. For the electrode configuration shown in FIG. 1, the equation (a condensation of Equation 8 of the reference) for motion parallel to the magnetic field is:

d' ulds (a q cos 2s) u 0 where a (4e V -lmw z d) i4 2 q RF u s rut/2 w The applied oscillator frequency where z The 2 distance of the electron from the center plane. (Motion in directions perpendicular to the magnetic field are of no significance to energy gain and so are not considered.)

1,, The anode hole radius divided by 1.6

d The anode cathode separation e Electronic charge m Electronic mass V Applied DC voltage V Applied RF amplitude and a superscript dot refers to differentiation with respect to s. The factor 1.6, by which the true anode hole radius is divided to yield Z is provided, as indicated in the referenced publication at page 2784, second column, line 7, thereof, to permit the use of a simplified but adequately accurate expression for the component of the electric field normal to the plane of the hole.

The best way of explaining the phenomenon of resonance energy gain is by relating it to the applied RF frequency and the natural electron oscillation frequency. The natural oscillation frequency of an electron in the electron confining region, having a given energy and oscillation amplitude, is determined by the configuration of the DC and RF fields. If the RF and natural electron oscillation frequencies are approximately equal, resonance is said to exist and the electrons gain energy from the RF field. Referring back to the discussion above in regard to FIG. 2, the meaning of the parametric coordinates being within an unstable region is that the two frequencies are sufficiently matched so that electron energy gain can occur.

With no RF voltage q= '0 and the equation of motion describes simple oscillation for electrons (i.e., simple harmonic motion for small amplitudes) in the electrostatic field. That oscillation frequency is given by (0 4e V /m z,,d The application of an infinitesimal RF voltage of frequency a) will cause resonance. effects if that applied frequency is some whole number multiple of the natural oscillation frequency w If the proportionality constant between the two frequencies is called a then the resonance can be written mathematically as a m (U 42 V /m 2 d. This expression for a is the same as that given at page 7, line 13 except that the term -l'4 has been omitted because'the present discussion deals with an infinitesimal RF voltage, corresponding to the horizontal axis of FIG 2, so that the electron is implicitly assumed to be considered static at z 2,, and its derivative under these idealized conditions (which are considered only as part of the explanation and are obviously not operating conditions) will be zero. Each unstable region shown on FIG. 2 represents one such resonance with a successively equalling l, 4, 9, etc. Thisrelation may be made more readily understandable by consideration of the mechanical analogue of a mass subject to an elasticrestoring force. The natural frequency of oscillation of such a mass is propor tional to the square root of the elasticconstant the restoring force for a given displacement. In the case of an electron, the restoring force for infinitesimal displacements producedby the DC field will be proportional to V so if V is multiplied by4, other parameters in a remaining the same, a will be multiplied by 4, and the natural frequency of the electron will be doubled, so that the RF frequency which will be resonant with hat infinitesimal amplitude will be doubled also. Similarly, if V is multiplied by 9, the resonantfrequency will be tripled.

Large values of the RF voltage tend to drag an electron into resonance even though its oscillation freabsence of applied RF does not vary linearlywith distance, but according to a hyperbolic tangent approximation.' In consequence, the resonant frequency of the electron is dependent upon the amplitude of its oscillations, and hence an applied RF field differing in frequency from the natural resonant frequency of the electrons for small amplitudes of oscillation can drive an electron to an amplitude of oscillation such that the electrons resonant frequency is altered to more nearly match that of the applied field. Since the electron resonant frequency is thus a function of the amplitude of its oscillation (that is, of its energy), once the electron has acquired energy such as to bring it into resonance with the applied RF field, any further addition of energy will alter its resonant frequency so that it is no longer resonant with the RF field, and it will tend to drop back in energy to remain resonant with the RF field. This leads to the result, discussed in more detail below, that the electrons subject to the combined static and RF electric fields will all, if the press is not interrupted by collision, come to the same energy. The amplitude of the RF field will determine the time required to reach this energy state; if it is too small to achieve this before the electrons are dissipated by collision, the desired result will not occur. Similarly, if it is not great enough to displace the electrons, on, the average, far enough to alter their resonant frequency to bring them into resonance with itself, this effect will not occur. This latter situation is represented by the stable areas of the Mathieu diagram of FIG. 2.

Thus the unstable'regions have significant width when the value of RF voltage is high. Any time the resonance just described exists, electrons can gain energy directly from the RF field through the resonancemode of energy growth. Using the dimensionless constants defined previously the electron energy grows exponentially as A m it 2 rmu e 2 where 1., the growth constant, is dependent upon the RF and DC voltages. The coordinates fixed by the values ofa and q on FIG. 2 thus tell whether electron energy growth takes place (i.e., when those coordinates are in an unstable region of the chart) and, through [.L, fix the rateof that growth. In an electrode configuration that gives a parabolic potential, all electrons in the space between the electrodes will oscillate with a single frequency and the electrons will stay in resonance and gain 'energy until they are stopped by collisions with gas atoms or the walls. Further information on the means for energizing electrons is contained in Radio Frequency Breakdown in a dc Parabolic Potential Field in Journal of Applied Physics, Yol. 36, No. l, l82 2,.lanuary 1965.

When the natural electron frequency changes with electron energy, as it does in the subject invention, resonance will no longer exist when the electron energy grows beyond a given limit; i.e.,'the natural frequency will have gone beyond the range consistent with electron energy gain. The electrons maximum energy can grow no farther than that limit becausethe resonance will no longer exist nor can it decrease, except for a short time, because this would once more allow reso-- nance to exist and cause energy gain back up to the limit. j

Mathematically this results in the addition of a velocity-dependent term (1 to the expression for a as specified. Consequently the coordinates a and q which represent on Mathieu Stability Chart the state of a given electron are time dependent.

As the electron gains energy; i.e., the velocity of the electron, 11, increases, its coordinates on the stability plot change. Consequently, if the RF and DC voltages are set so that a zero energy electron starts on the right side of an unstable region (denoted as l) in FIG. 2) an electron can gain energy until its a coordinate places it on the left side of tbe same region (denoted as (2) in FIG. 2.). From there all energy gain must be through the collisional mode. However, no significant energy would be gained in this way once the electron energy is high enough since the collisions necessary for energy growth in this mode would lead to excitation of the background gas and a marked energy loss. As soon as an electron has lost in the excitation process the energy gained from the applied fields, its coordinates on the stability chart revert to the right side of the unstable region at (l) where it can begin the process again. The

molecules or atoms excited bythese electrons will form' an inverted population and are induced through stimulated emission to drop to a lower energy state by emitting a photon coherently with the stimulating radiation.

The width of an unstable region in FIG. 2 at a given RF voltage amplitude thus determines the maximum amount of energy an electron can gain in the resonance mode. The length of this horizontal line measured from right to left as between I and 2 on FIG. 2, is proportional to the maximum possible energy gain of an electron. If the required energy gain is then specified the length of the line that will be used is specified. This specified line length is measured off along a line determined by the specified RF voltage amplitude. The rightmost end of the measured line specifies the starting point, and, by reference to its position along the abscissa, also specified the desired DC voltage. The specified energy gain must be less than or equal to the maximum energy gain in the specified unstable region at the given RF voltage amplitude. If this is not so, a different unstable region or different (generally higher) RF voltage amplitude must be used.

The constants in the equations are fixed in the following manner. The dimensions of the apparatus z,, and d are set by the physical volume in which lasing is desired. The RF frequency should be as large as possible to hasten electron energy growth. Since this energy growth must take place between collisions, high pressures require high RF frequency. The only limitations on frequency are the availability of an appropriate RF oscillator and the size of the DC voltage. Since 4 e V,,,;/mw z,,d must be the order of one, can be large only if V is large. Unfortunately high DC voltages will induce a Penning discharge and thus destroy the electron energy distribution. Thus, V should be set just below the voltage ranges that cause a Penning discharge, as can be determined experimentally, and a) will be set by the value of the coordinate a that is desired as a starting point (i.e., (l) on FIG. 2). The RF voltage V is then also fixed since q is also set by that desired starting point.

Because there is a relation between the power input, the RF voltage applied, and impedance of the electrode configuration, there may be a limitation on what starting coordinates are available. Ideally one would like to operate in the broadest part of the unstable region (so that low energy growth rates found near the edge of the unstable region can be avoided), but the RF voltages and power levels required may not be practicable with available equipment. Thus, in practice, the attainable value of V may determine the initial operating point.

A graphical technique of design would then require a guess at a starting point within an unstable region (i.e., pick a and q). The first unstable region is preferred because higher growth rates can be obtained with lower RF voltages in this region of the stability chart (FIG. 2) than in any other. Values of and d will be fixed by the volume to be excited. Then the energy of the quantum state to be excited is specified in relation to the gas used which fixes the electron energy gain needed. If the fraction of the width of the unstable region to be used is then picked (e.g., 80 percent then if can be measured off of FIG; 2.

The RF frequency can then be determined from w dz/dt Z/z,,u where dz/dt is the electron velocity desired. The value of V can then be determined from V mw z dal ie and V from V mw z dq/4e. If V is above the Penning discharge limit or V above what can be obtained with the available oscillator another starting coordinate must be chosen. In sequence (0, V and V can then be redetermined until practically realizable values are obtained. The excitation process of the subject invention will not take place ifa Penning discharge occurs.

Looking again at the apparatus shown in FIG. 1, the magnetic field induced in solenoid 32 (or by permanent magnets, if desired) is adjusted in magnitude so that electrons near the edge of anode hole 30 will collide with anode 28 because of their Larmor radius. If permanent magnets are to be used, the magnetic field can be adjusted to the desired value by the placement, quantity and type of magnet used. In this way only electrons near the center of hole 30 where the axial potential distribution changes very little will take part in the energy gain process. If the magnetic field were not so adjusted, the maximum energy electrons attained would be a function of their radial position and hence there would not be a sharp limit to the electron energy.

The apparatus shown in FIG. 1 provides a given limit to the electron energy at only one position, within the anode plane. At axial positions other than the anode plane, electrons will have lower kinetic energies and so be capable of exciting lower lying excitation states. The effective electron energy distribution will therefore have a large low energy component with resultant energy losses due to excitation of undesired states. It is only when the state to be excited is a lowest lying state that the low energy electrons will be unimportant.

The simple planar electrode configuration as shown in FIG. 1 is thus more effective in pumping than an ordinary discharge primarily when the state to be excited is a lowest lying state. Primarily, the subject invention's advantage over the use of pure collisional energy is that the sharp upper limit of the electron energy eliminates any high energy tail.

In order to minimize the effect of these low energy electrons a drift tube 38 may be substituted for planar anode 28 of FIG. 1. Drift tube 38, as shown in FIG. 3, is substantially cylindrical in shape and is comprised of an outer cylindrical member 38a, a concentric inner cylindrical member 38b located within the interior of laser 10 and two annular, flat members 38c joining the inner and outer cylinders 38a, 38b at the ends thereof. The other apparatus of the laser is the same as that shown in FIG. 1.

By use of drift tube 38, the high energy electrons can be kept at that high energy level for a large part of their trajectory. Energy gain occurs in the space 40 between the anode and the cathodes. Since most of the electrons will be within the drift tube at any given time because drift tube 38 extends almost the entire length of the laser interior, they therefore will nearly all have the same energy, and the discharge may be treated as a nearly monoenergetic source of electrons.

Another advantage of this embodiment is that ionization of the electron source, which is preferably a material such as cesium, predominantly takes place within drift tube 38, thereby extending the lifetime of the neutralizing ions. The presence of these neutralizing ions also allows the use of higher electron densities than mightotherwise be possible.

As the apparatus shown in FIG. 3 can be used to excite atomic or molecular energy levels above the lowest energy state, it is desirable that the electrical parameters be adjusted so that the narrow electron energy distribution matches a desired higher atomic or molecular energy level.

The following description is a more quantitative explanationof how the parameters can be adjusted to provide the desired excitation as generally described above and as graphically shown in FIG. 2. The maximum energy, E,,,, that an electron can gain in the first unstable region of the chart shown in FIG. 2 given by E,,,= mz,, w Q,/ where This represents the length of the line analogous to (1 (2) in FIG. 2 but within the first unstable region. For practical reasons only a fraction of this maximum energy'should be used. The DC electrode potential that must be used to allow an electron to reach a given energy, E E,,, must thenbe given by V =m w dz,,/4e (Q, ale/13mm) where =1qq 18+q 64... This value of V can be looked upon as the potential well depth that is required to keep the electron oscillation frequency in resonance with the RF frequency over a change in electron energy of E.

The above equation with the expression for q given earlier determines the values of the electrical parameters V and V that must be used to produce a narrow electron energy distribution of energy. E in an electrode configuration such as that shown in FIG. 1 or 2. One skilled in the art can determine appropriate values for q, to, and the dimensional factors d and z... The primary considerations in their determination follow. The magnitude of the factor q must be kept in the range of 0.5 to 2 to insure rapid electron energy gain and practical values of V The electrode dimensions z,,, d, and the drift tube length are set by the size of the gas volume that is to be excited, with the limitation that d/z l so that electron excursions are held within tolerable bounds. Finally, the value of m, the RF frequency, must be kept high to maximize the electron energy gain rate but not so high as to make values of V and V impractically high. All of this is within the present state-of-the art.

The procedure for configurations differing from those shown in FIGS. 1 and 3 would be very similar. Modifications iri the form of. FIG. 2 and hence inthe terms Q, and Q would be needed. Otherwise there will be no fundamental change.

Parameters determined in this way have been applied to an experiment in which selective excitation of the B Zu" state of the nitrogen molecular ion was sought. The experimental requirements were Electron Energy -d-z,,

1.5 X 10 hz1.2 I20 volts190 volts The electrical energy of a discharge using these parameters resulted in the excitation of the B if state alone. If a similar application is made to a state which is the upper member of a laser transition, efficient laser action can be expected.

For operation of the embodiment shown in FIG. 3, the magnetic field is positioned to restrict the electron region to a substantially cylindrical shape located substantially coaxially within cylindrical drift tube 38. The

magnitude of this field limits the bulk of the electrons to a diameter somewhat less than the diameter of inner cylindrical portion 38b of the drift tube. Operation of the above-mentioned embodiment is substantially the same as that described in regard to the embodiment shown in FIG. 1.

If desired, other drift tube configurations may be used. For example, the same structure as that shown in FIG. 3 could be used, but withoutthe inner cylindrical member 38b. Also, the inner cylindrical member 38!) could be replaced by a cylindrical wire grid or a plurality of axially extending annular members located in a substantially cylindrical array. Another alternative configuration would be to have a plurality of hollow annular members each having a rectangular cross-section and spaced in a cylindrical array having axially extending spaces therebetween. Each of these annular members would, of course, be electrically connected to one another and to the power supply. The above-mentioned configurations are particularly useful for experimental applications of the laser so thatone or more probes may be easily positioned within the discharge region of the drift tube.

It is desirable in many applications of a laser to have a quick recovery time; i.e., to have as short a period of I experienced in matching the load to an RF source,

thereby resulting in only a portion of the RF energy applied to the laser being utilized to energize the electrons.

A third and preferred embodiment, as shown in FIGS. 4, 5 and 6, utilizes resonant cavities 42, 44 to remedy the above-noted limitations while maintaining the advantages as discussed in relationship to the embodiment in FIG. 3. As shown therein, the laser includes two resonant cavities 42, 44 each of which is hollow and has a similar box-like shape with one open side. Cavities 42, 44 are located in substantially parallel opposed relationship to one another. A substantially solid and thick center wall 46 is located parallel to and between the two cavities 42, 44 and separated from each of the cavities by thin electrically insulating strips 48, 50 positioned inside the perimeter of the center wall. Center wall 46 and insulating strips 48, 50 serve to close up the open side of each of cavities 42, 44 and make the interior of the device air tight. Strips 48, 50 are thin enough to not interfere with RF fields in the cavity walls, while allowing a separate DC bias to be impressed on center wall 46.

The important portions of the interior of the laser are shown by dotted lines in FIGS. 4 and 5. An elongated, rectangular slot 52 is centrally located in center wall 46. Cylindrical bores 54, 55 aligned with the longitudinal axis of slot 52 extend from each end thereof to an end of the center wall. Across the end of bore 54, a mirror (reflector) 56 having a reflectivity substantially less than I00 percent is located. A second mirror 58, having a reflectivity of approximately 100 percent, is located across the end of bore 55.

If desired, suitable means may be provided for matching the cavities to the RF signal. Also, a gas fill and vacuum system 64 is connected to one of the cavities 42 to perform a function similar to system 36 of FIG. 1.

Center wall 46 acts as an anode and cavities 42, 44 as cathode for the DC voltage from DC power supply 67. An oscillator 65 which provides the desired RF signal is electrically coupled to each of the two resonant chambers 42, 44 in a manner well known in the art. Solenoid coil 66 is circumferentially disposed about the width of the laser apparatus and is suitably connected to an electrical power supply so as to provide a uniform magnetic field within slot 52. Of course, if desired, permanent magnets may be used to provide the magnetic field.

Slot 52 in center wall 46 allows electrons to pass from one resonant cavity to the other along magnetic field lines and will approach field-free conditions or drift region, which is somewhat comparable to the area within the drift tube described in regard to the embodiment shown in FIG. 3. One major distinction from the embodiment of FIG. 3 is that while in both embodiments (FIG. 3 and FIG. 4) the lasing region runs the length of drift tube 38 or slot 52, in the embodiment of FIGS. 4 and 5, the pumping electrons drift transverse to slot 52. Thus, the drift space is much smaller in the present embodiment and, therefore, the average electron can increase the number of excitations per second it can make by more than an order of magnitude.

Operation of the laser shown in FIGS. 4 and 5 is similar to that discussed in regard to the embodiments of FIGS. 1 and 3. DC voltage of a given amplitude is applied between the anode (center wall 54) and the cathodes (resonant chambers 42, 44) to produce an electric field within the cavities. Standing waves are then set up within the cavities by means of oscillator 65 to cause resonant excitation of the electrons within the lasing region which in turn causes an inverted population in the excited states of the background gas which produces stimulated emission of photons within this region. These photons leave through bore 54 in center wall 52. The RF and DC voltages to be used are obtained by reference to a Mathieu chart similar to that shown in FIG. 2 and the analysis discussed above in relationship thereto.

Also of importance in regard to the operation of the subject invention and the Mathieu stability chart is the field configuration, i.e., distribution. For analysis of the field distribution it is desirable to take a coordinate system with the x co-ordinate taken perpendicular to the plane of the large side of the cavity, the y coordinate along the cavity width and the z coordinate along the length of the cavity as shown in FIGS. 4 and 5. Using the TE mode in a cavity having a small x dimension and y and 2 dimensions comparable to half a wave length (the cavity width being designated as b and the cavity length being designated as d) the equations are as follows: where E electric field H magnetic field [L permeability of free space C velocity of light k wave number =21r/A k the cutoff wave number which is the inverse of the limiting wavelength that the cavity can maintain j phase shift E jwnC/k rr/b sin rry/b sin rrz/d H,, C/k, (11 /dk sin Try/b cos rrz/d Utilizing the above-mentioned equations, the structure can be designed so as to create a substantially uniform field along the entire slot length. Considering the slot width (in the y direction) to be quite small as compared to b, the width of cavities 42, 44, the electric field amplitude will change little across the slot. Since the slot length lies in the z direction, the electric field will generally change with sin (n'z/d). However, ifb changes with z in an inverse sine relationship over the region near 1 equals d/2, E can be kept constant over much of the slot length while using most of the length of the chamber d.

Thus, if

b b lsin (rrz/d) E =jwpf'O/1TC sin 7ry/b However, near z =0 or z d, the cavity width should become infinite. As this, of course, is not feasible, the slot length must be shorter than the cavity length. By predetermining the ratio of the minimum width of the cavity to the maximum width of the cavity, i.e., b lb the maximum length and position of the slot relative to the cavity can be determined. For example,

0.1655 d; correspondingly 2 (1 0.1655) d 0.8345 d. Therefore, the middle 67 percent of the length of the cavity could be utilized. For b lb fix, z =d/1r sin A; 0.108d and z 0.892d.

In this case approximately the middle 78 percent of the length of the cavity could be used for the slot to provide a constant electric field. In the structure shown in FIG. 4 the width, b, of each of cavities 42, 44 adjacent to slot 52 varies in accordance with the equation b b /sin(1rz/d) with the minimum width of each cavity (b being approximately one half of the maximum width of the cavurnt)- The problem of transmitting RF energy to the lasing region i.e., the slot is eliminated by the use of resonant cavities which avoid the problem of reflection in the transmission line. Therefore, the RF source, which in this case is oscillator 65, must only supply as much power as cavities 42, 44 and electron energization dissipate to keep the fields at a desired amplitude. Little power is reflected at the RF couplings and overall power efficiency is greatly improved.

A further advantage of the preferred embodiment is that the cavities are a natural method of using high frequency microwaves which thereby permits the use of higher frequency microwaves ad therefore an increased growth rate of electron energy allowing more excitations per second for each electron. Also, the use of higher frequencies permits the size of the slot to be reduced, which, with a given RF voltage amplitude, de-

creases minimum drift space length, thereby further increasing the energy growth rate. Also, higher RF frequencies allow penetration of more dense plasmas, i.e., more electrons per unit volume and higher ultimate laser powers.

While three particular electrode embodiments have been shown in the drawings many other electrode embodiments may be used to provide a desired electric field configuration.

By use of the subject invention, emission of high intensity electromagnetic radiation in the infrared, visible, ultraviolet or even soft x-ray wave lengths can be obtained.

While the subject invention has been particularly described for use in pumping a laser, it also may be used to cause emission of non-coherent narrow frequency band radiation for use in a lamp for providing infrared, ultraviolet or visible light or an x-ray emitter. The narrow energy distribution of the electrons can also be useful in other applications such as chemical synthesis.

Thus the subject invention provides apparatus and method for causing resonant excitation of electrons to cause excitation of background gas atoms and emission of coherent or non-coherent high intensity radiation by effecting an RF discharge of a desired voltage and frequency to occur within an electron containing region defined by both a magnetic and electric field of predetermined intensity.

It is obvious to one skilled in the art that many modificiations may be made to the subject invention without departure from the scope thereof.

What is claimed is:

1. The method of exciting electrons to a predetermined energy by the use of apparatus comprising:

a. an enclosure containing a gas;

LII

b. means for providing electrons within the said enclosure;

c. means for providing a constant electric field component within the enclosure to form a potential well for electrons, of such spatial variation that the force tending to move an electron to the lowest point of the well varies nonlinearly with its displacement therefrom;

d. means for providing a magnetic field of direction and magnitude appropriate to direct moving electrons toward the said well;

e. means for providing an alternating electric field component in the said potential well to vary its depth cyclically;

which method comprises the improvement of f. adjusting the magnitude of the constant electric field component and the magnitude and frequency of the alternating electric field component to lie within an instability region of the Mathieu diagram representing the operational characteristic of the apparatus, and distant from the left-hand boundary of that instability region by a horizontal distance corresponding to the said predetermined energy.

2. The method claimed in claim 1, by the use of apparatus in which the means c) comprises a pair of opposed cathodes and an anode having an aperture located therebetween, and a source of constant electric potential connected to the two cathodes via common connection between them, and to the anode;

the means d) provides a magnetic field in the direction from one cathode to the other which passes through the anode aperture;

the means e) comprises an alternating electric potential source connected to the two cathodes. 

1. The method of exciting electrons to a predetermined energy by the use of apparatus comprising: a. an enclosure containing a gas; b. means for providing electrons within the said enclosure; c. means for providing a constant electric field component within the enclosure to form a potential well for electrons, of such spatial variation that the force tending to move an electron to the lowest point of the well varies nonlinearly with its displacement therefrom; d. means for providing a magnetic field of direction and magnitude appropriate to direct moving electrons toward the said well; e. means for providing an alternating electric field component in the said potential well to vary its depth cyclically; which method comprises the improvement of f. adjusting the magnitude of the constant electric field component and the magnitude and frequency of the alternating electric field component to lie within an instability region of the Mathieu diagram representing the operational characteristic of the apparatus, and distant from the left-hand boundary of that instability region by a horizontal distance corresponding to the said predetermined energy.
 2. The method claimed in claim 1, by the use of apparatus in which the means c) comprises a pair of opposed cathodes and an anode having an aperture located therebetween, and a source of constant electric potential connected to the two cathodes via common connection between them, and to the anode; the means d) provides a magnetic field in the direction from one cathode to the other which passes through the anode aperture; the means e) comprises an alternating electric potential source connected to the two cathodes. 